Zero slope

When you understand that the slope of a line is a way of describing the “steepness” of a line, it is easy to see why a line may have positive or negative slope. But why might a line have zero slope, and what kinds of lines will always have a slope of zero? We will explore these ideas in the following lesson.

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What kinds of lines have zero slope?

Any line of the form \(y = c\), where \(c\) is some real number, will have a slope of zero. The lines are horizontal (flat) and so have no “steepness” to measure.

Why do horizontal lines have slopes of zero?

Let’s use the line graphed above, \(y = 2\), to understand why a line like this will always have zero slope. Pick two points on the line from the graph, say \((1, 2)\) and \((2,2)\). We can let \((x_1, y_1) = (1,2)\) and \((x_2, y_2) = (2,2)\) and apply the slope formula: